Thus, In A Sense, Mathematics

The Presentation Of Mathematics In Schools Should Be Psychological And Not Systematic. The Teacher, So To Speak, Should Be A Diplomat. He Must Take Account Of The Psychic Processes In The Boy In Order To Grip His Interest, And He Will Succeed Only If He Presents Things In A Form Intuitively Comprehensible. A More Abstract Presentation Is Only Possible In The Upper Classes.

The Developing Science Departs At The Same Time More And More From Its Original Scope And Purpose And Threatens To Sacrifice Its Earlier Unity And Split Into Diverse Branches.

Thus, In A Sense, Mathematics Has Been Most Advanced By Those Who Distinguished Themselves By Intuition Rather Than By Rigorous Proofs.

Every One Who Understands The Subject Will Agree That Even The Basis On Which The Scientific Explanation Of Nature Rests Is Intelligible Only To Those Who Have Learned At Least The Elements Of The Differential And Integral Calculus, As Well As Analytical Geometry.

Mathematics In General Is Fundamentally The Science Of Self-evident Things.